A193102 - OEIS

%I #10 Feb 21 2025 16:43:41

%S 1,8,71,478,3248,19674,116885,655064,3602627,19082622,99353815,

%T 503974610,2518347829,12341129010,59691674707,284343349874,

%U 1339171125620,6229010760982,28686750790598,130740792179088,590661906472634,2644740541614160

%N G.f.: exp( Sum_{n>=1} 2*sigma(n*3^n)*x^n/n ).

%e G.f.: A(x) = 1 + 8*x + 71*x^2 + 478*x^3 + 3248*x^4 + 19674*x^5 +...

%e log(A(x)) = 8*x + 78*x^2/2 + 242*x^3/3 + 1694*x^4/4 + 4368*x^5/5 + 19680*x^6/6 + 52480*x^7/7 +...+ 2*sigma(n*3^n)*x^n/n +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, 2*sigma(m*3^m)*x^m/m)+x*O(x^n)), n)}

%Y Cf. A176310, A193103, A193104.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 15 2011